cp's OEIS Frontend

A170041 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170041 #8 Nov 26 2016 09:45:52
%S A170041 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A170041 27292513198112,846067909141472,26228105183385632,813071260684954592,
%U A170041 25205209081233592352,781361481518241362912,24222205927065482250272
%N A170041 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170041 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A170041 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170041 <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
%F A170041 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170041 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170041 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170041 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4
%F A170041 + 2*t^3 + 2*t^2 + 2*t + 1)/(465*t^36 - 30*t^35 - 30*t^34 - 30*t^33 -
%F A170041 30*t^32 - 30*t^31 - 30*t^30 - 30*t^29 - 30*t^28 - 30*t^27 - 30*t^26 -
%F A170041 30*t^25 - 30*t^24 - 30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 - 30*t^19 -
%F A170041 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 -
%F A170041 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4
%F A170041 - 30*t^3 - 30*t^2 - 30*t + 1)
%t A170041 With[{num=Total[2t^Range[35]]+t^36+1,den=Total[-30 t^Range[35]]+ 465t^36+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Oct 19 2012 *)
%K A170041 nonn
%O A170041 0,2
%A A170041 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009